Fluid Mechanics help

Hey, I'm working on programming a Newtonian mechanics engine (not as part of coursework, btw, for a game that I'm making).

I have some problems, however, as to how to approach fluid mechanics. I know a little bit: buoyant forces, specific gravity, and such. However, I just do not get the more complex (and hence what I need to program) equations and math for viscosity, Newtonian fluids, and such.

Could someone help me understand the basic nature of the following? (I have up to a calculus II knowledge and I know pretty much all of basic, general physics)

1. Sheer stress
2. Fluid viscosity constant --why is it in Pa*s?
3. Can someone give me a good idea of what a gradient is? I understand that mathematically it's a needed idea, and I get the concept of the partial derivative decently well (Though a little help there would be nice, too).
4. What does Newton's partial differential equation for Newtonian fluids mean in words? What does tao signify? (tao = eta*partial derivative(u) of y)